The asnwer is 2.04% for the w/v solution and 1.94% for the v/v solution.
Let's start by clearly defining what our solutions look like.
A w/v solution is usually used when a dry chemical is mixed as a dry mass (grams) per volume (mL), where
number.of.grams100mL = percent concentration
So, a 5% w/v solution will have 5g of a substance in 100mL of ethanol.
A v/v solution is used when dealing with liquid reagents and it represents
number.of.mL100mL = percent concentration
So, a 5% v/v solution will have 5mL of a substance in 95mL ethanol.
Now, let's start with the w/v solution. An initial 5% concentration is now brought to 0.1%; this means that the volume of the solution is now 50 times larger (since the concentration is 50 times smaller).
Therefore, the 5g of the substance would now occupy
50⋅100mL=5000mL, out of which only the initial 100mL would represent ethanol (since the initial solutions are diluted in saline). The percentage of ethanol in the final solution would be
100mL(5000−100)mL⋅100%=2.04%
The procedure is similar for the v/v solution; the initial 5% solution's volume will now be 50 times larger, which means that the 5g of substance will now occupy
50⋅100mL=5000mL, out of which 95mL would represent ethanol. The percentage of ethanol would now be
95mL(5000−95)mL⋅100%=1.94%
